Analysis Techniques: Flood Analysis Example with Instaneous Peak Flow Data (Log-Pearson Type III Distribution)

Information to get started:
  • The lesson below contains step-by-step instructions and "snapshots" of what each step looks like when carried out in a Microsoft Excel workbook. Blue shading of information in the Excel illustrations denotes changes made from the previous step. Dots placed in three consecutive rows indicate that a portion of data is hidden from sight.
  • You can download an Excel workbook containing the complete data set by clicking on the "Download Data" link below. It contains each calculation step on a separate worksheet. To move between steps, click on the tabs at the bottom of the excel window.
  • When you download the file, it may open in your browser window. You may wish to use the "save as" function to save the file to a local drive and then reopen it in Excel. This will make it easier to flip between the online lesson and the example workbook.
  • Finally, we want to remind you that the techniques explained on this site are statistically based; therefore results must be viewed as predictions and not as facts. Please use the techniques and the information obtained from them responsibly!

Download Data

View and print this webpage as a pdf file.

Step 1: Obtain streamflow data

Obtain instantaneous peak streamflow data from the USGS web site.

  • Go to
  • Select Historical Water Data
  • Select Surface Water
  • Select Peaks
  • Check box under Site Identifier for Site Name and Submit
  • Type in Alsea under Site Name and select match any part and Submit
  • Select gage at TIDEWATER (140306500)
  • Select Tab-separated data
  • For the example, copy entire data set into Excel worksheet
  • Paste special as text (this will separate the data into columns)

Step 2: Organize the information in a table.

Step 3: Rank the data from largest discharge to smallest discharge.

  • Add a column for Rank and number each streamflow value from 1 to n (the total number of values in your dataset).

Step 4: Create a column with the log of each max or peak streamflow using the Excel formula {log (Q)} and copy command.

Step 5: Calculate the Average Max Q or Peak Q and the Average of the log (Q)

Step 6: Create a column with the excel formula {(log Q avg(logQ))^2}

Step 7: Create a column with the excel formula {(log Q avg(logQ))^3

Step 8: Create a column with the return period (Tr) for each discharge using Excel formula {(n+1)/m}. Where n = the number of values in the dataset and m = the rank.

Step 9: Complete the table with a final column showing the exceedence probabilityof each discharge using the excel formula {=1/Return Period or 1/Tr} and the copy command.

Step 10: Calculate the Sum for the {(logQ avg(logQ))^2} and the {(logQ avg(logQ))^3} columns.

Step 11: Calculate the variance, standard deviation, and skew coefficient as follows:

variance =

standard deviation =

skew coefficient =

Excel functions can also be used to calculate the variance (=VAR( ) ), standard deviation (=STDEV( ) ), and skewness coefficient (=SKEW( ) ). Note that you use these formulas with the data in the log(Q) column.

Step 12: Calculate weighted skewness

Show Me

Step 13: Calculate k values

  • Use the frequency factor table and the skew coefficient to find the k values for the 2,5,10,25,50,100, and 200 recurrence intervals.
  • If the skew coefficient is between two given skew coefficients in the table than you can linearly extrapolate between the two numbers to get the appropriate k value. To view the frequency factor table click on the "show me" link below.

Show Me

Step 14: Using the general equation, list the discharges associated with each recurrence interval

general equation =

Step 15: Create table of Discharge values found using the log Pearson analysis

Step 16: Create Plot

Below is a comparison of flood frequency analysis completed using mean daily data versus instantaneous discharge data. As can be seen, had you completed this analysis using mean daily data, the result would have been an underestimation of the discharges associated with each return period.

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